Zero-temperature Susceptibility Research Articles

Ground state magnetic susceptibility of Kondo impurities

Impurity models describe localized impurities interacting with the spins of electrons. Strong correlations lead to non-trivial behaviours of the model. In this work we present 3 different impurity models: (1) the single-impurity Kondo model; (2) the two-impurity Kondo model; (3) the two-channel Kondo model. For each model we present a spin chain emulation and utilize the density matrix renormalization group (DMRG). We study the magnetization and zero-temperature susceptibility of the impurity when a local magnetic field is applied. We get the expected relations theoretically.

Equipartition of the entanglement entropy

The entanglement in a quantum system that possess an internal symmetry, characterized by the Sz-magnetization or U(1)-charge, is distributed among different sectors. The aim of this letter is to gain a deeper understanding of the contribution to the entanglement entropy in each of those sectors for the ground state of conformal invariant critical one dimensional systems. We find surprisingly that the entanglement entropy is equally distributed among the different magnetization sectors. Its value is given by the standard area law violating logarithmic term, that depends on the central charge c, minus a double logarithmic correction related to the zero temperature susceptibility. This result provides a new method to estimate simultaneously the central charge c and the critical exponents of U(1)-symmetric quantum chains. The method is numerically simple and gives precise results for the spin-1/2 quantum XXZ chain. We also compute the probability distribution of the magnetization in contiguous sublattices.

Nematic fluctuations in iron-based superconductors studied by resistivity change under uniaxial pressure

Antiferromagnetic, nematic and superconducting phases have been widely found in iron-based superconductors. The study on their relationships is thus crucial for understanding the low-energy physics and high-temperature superconductivity. The so-called nematic phase represents a spontaneous in-plane rotational symmetry breaking of the electronic states, which results in strong in-plane anisotropic properties. We have developed a uniaxial pressure device, which enables us to obtain nematic susceptibility by studying the resistivity change under uniaxial pressure at low temperature. In this paper, we brief two of our recent researches on nematic fluctuations in iron-based superconductors. The first research shows the presence of a nematic quantum critical point in BaFe2-xNixAs2, which exhibits several characteristics, including the zero mean-field nematic transition temperature x=0.11, broad hump feature in the nematic susceptibility in overdoped samples, strongest nematic susceptibility along the (100) direction at x=0.11, and the divergence of zero-temperature nematic susceptibility at x=0.11 for uniaxial pressure along both the (110) and (100) directions. We further study the nematic susceptibility in many other iron-based superconductors and find that the ordered moment at zero temperature linearly scales with nematic Curie constant, which is obtained from the Curie-Weiss-like temperature dependence of nematic susceptibility in these materials. Accordingly, we propose a universal phase diagram for iron-based superconductors, where superconductivity is achieved by suppressing the long-range antiferromagnetic order in a hypothetical parent compound though the enhancement of nematic fluctuations by doping, including both carrier doping and isovalent doping. Our results suggest that nematic fluctuations play a very important role in both the antiferromagnetism and superconductivity in iron-based superconductors.

Critical charge instability on the verge of the Mott transition and the origin of quantum protection in high-Tccuprates

The concept of topological excitations and the related ground state degeneracy are employed to establish an effective theory of the superconducting state evolving from the Mott insulator for high-${T}_{c}$ cuprates. The theory includes the effects of the relevant energy scales with the emphasis on the Coulomb interaction $U$ governed by the electromagnetic U(1) compact group. The results are obtained for the layered $t\ensuremath{-}{t}^{\ensuremath{'}}\ensuremath{-}{t}_{\ensuremath{\perp}}\ensuremath{-}U\ensuremath{-}J$ system of strongly correlated electrons relevant for cuprates. Casting the Coulomb interaction in terms of composite-fermions via the gauge flux attachment facility, we show that instanton events in the Matsubara ``imaginary time,'' labeled by topological winding numbers, are essential configurations of the phase field dual to the charge. This provides a nonperturbative concept of the topological quantization and displays the significance of discrete topological sectors in the theory governed by the global characteristics of the phase field. We show that for topologically ordered states these quantum numbers play the role of an order parameter in a way similar to the Landau order parameter for conventionally ordered states. In analogy to the usual phase transition that is characterized by a sudden change of the symmetry, the topological phase transitions are governed by a discontinuous change of the topological numbers signaled by the divergence of the zero-temperature topological susceptibility. This defines a quantum criticality ruled by topologically conserved numbers rather than the Landau principle of the symmetry breaking. We show that in the limit of strong correlations topological charge is linked to the average electronic filling number and the topological susceptibility to the electronic compressibility of the system. We exploit the impact of these nontrivial U(1) instanton phase field configurations for the cuprate phase diagram which displays the ``hidden'' quantum critical point covered by the superconducting lobe in addition to a sharp crossover between a compressible normal ``strange metal'' state and a region characterized by a vanishing compressibility, which marks the Mott insulator. Finally, we argue that the existence of robust quantum numbers explains the stability against small perturbation of the system and attributes to the topological ``quantum protectorate'' as observed in strongly correlated systems.

Orbital magnetic susceptibility of disordered mesoscopic systems

In this paper we study the orbital weak-field susceptibility of two-dimensional diffusive mesoscopic systems. For the previously unstudied regime of temperatures lower than the mean level spacing we find unexpected strong temperature as well as statistical ensemble dependence of the average and typical susceptibilities. An explanation for these features is given in terms of the long tail of the zero-temperature susceptibility distribution, including the parametric form of the temperature dependence. For temperatures higher than the mean level spacing we calculate the difference between the true canonical ensemble and the effective grand-canonical ensemble. We also perform numerical simulations, which seem to generally confirm previous theoretical predictions for this regime of temperatures, although some difficulties arise. The important role of gauge-invariance, especially how it renders Random Matrix Theory inapplicable to the study of orbital susceptibility, is discussed. We conclude by considering interaction effects, giving a new interpretation to previous results as well as demonstrating the influence of in-plane magnetic field on the interaction-induced orbital response.

The Numerical Study of the S = 1/2 XXZ Chain**The project supported by National Natural Science Foundation (No. 19975031) and the RFDF (No. 1999024833) of China

We adopt the Lanczos method combined with the quantum conformal field theory to investigate the S = 1/2 XXZ chain in detail. The bulk-limit ground state energy, the anomalous scaling dimension of the spin operators, the Fermi velocity and the zero-temperature susceptibility are numerically calculated. The results agree to the exact solution well.

Energy landscapes in random systems, driven interfaces, and wetting

We discuss the zero-temperature susceptibility of elastic manifolds with quenched randomness. It diverges with system size due to low-lying local minima. The distribution of energy gaps is deduced to be constant in the limit of vanishing gaps by comparing numerics with a probabilistic argument. The typical manifold response arises from a level-crossing phenomenon and implies that wetting in random systems begins with a discrete transition. The associated "jump field" scales as <h> approximately L-5/3 and L-2.2 for (1+1) and (2+1) dimensional manifolds with random bond disorder.

The asymmetric single-impurity Anderson model – the modified perturbation theory

We investigate the single-impurity Anderson model by means of the recently introduced modified perturbation theory. This approximation scheme yields reasonable results away from the symmetric case. The agreement with exactly known results for the symmetric case is checked, and results for the non-symmetric case are presented. With decreasing conduction band occupation, the breakdown of the screening of the local moment is observed. In the crossover regime between Kondo limit and mixed-valence regime, an enhanced zero-temperature susceptibility is found.

Critical Behavior and Griffiths-McCoy Singularities in the Two-Dimensional Random Quantum Ising Ferromagnet

We study the quantum phase transition in the two-dimensional random Ising model in a transverse field by Monte Carlo simulations. We find results similar to those known analytically in one-dimension. At the critical point, the dynamical exponent is infinite and the typical correlation function decays with a stretched exponential dependence on distance. Away from the critical point there are Griffiths-McCoy singularities, characterized by a single, continuously varying exponent, z', which diverges at the critical point, as in one-dimension. Consequently, the zero temperature susceptibility diverges for a RANGE of parameters about the transition.

Theory of magnetic short-range order for high- Tc superconductors

A theory of magnetic short-range order for high- T c cuprates is presented on the basis of the one-band t− t′-Hubbard model combining the four-field slave-boson functional integral technique with the Bethe cluster method. The groundstate phase diagram evaluated self-consistently at the saddle-point and pair-approximation levels shows the experimentally observed suppression of magnetic long-range order in the favour of a paraphase with antiferromagnetic short-range order. In this phase the uniform static spin susceptibility consists of interrelated itinerant and local parts and increases upon doping up to the transition to the Pauli paraphase. Using realistic values of the Hubbard interaction we obtain the cusp position and the doping dependence of the zero-temperature susceptibility in reasonable agreement with experiments on La 2−δSr δCuO 4.

Spin susceptibility and magnetic short-range order in the Hubbard model.

The uniform static spin susceptibility in the paraphase of the one-band Hubbard model is calculated within a theory of magnetic short-range order (SRO) which extends the four-field slave-boson functional-integral approach by the transformation to an effective Ising model and the self-consistent incorporation of SRO at the saddle point. This theory describes a transition from the paraphase without SRO for hole dopings \ensuremath{\delta}\ensuremath{\gtrsim}${\mathrm{\ensuremath{\delta}}}_{{\mathit{c}}_{2}}$ to a paraphase with antiferromagnetic SRO for ${\mathrm{\ensuremath{\delta}}}_{{\mathit{c}}_{1}}$${\mathrm{\ensuremath{\delta}}}_{{\mathit{c}}_{2}}$. In this region the susceptibility consists of interrelated ``itinerant'' and ``local'' parts and increases upon doping. The zero-temperature susceptibility exhibits a cusp at ${\mathrm{\ensuremath{\delta}}}_{{\mathit{c}}_{2}}$ and reduces to the usual slave-boson result for larger dopings. Using the realistic value of the on-site Coulomb repulsion U=8t for ${\mathrm{La}}_{2\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$${\mathrm{Sr}}_{\mathrm{\ensuremath{\delta}}}$${\mathrm{CuO}}_{4}$, the peak position (${\mathrm{\ensuremath{\delta}}}_{{\mathit{c}}_{2}}$=0.26) as well as the doping dependence reasonably agree with low-temperature susceptibility experiments showing a maximum at a hole doping of about 25%. \textcopyright{} 1996 The American Physical Society.

Molecular-field theory of moment reduction in Kondo systems with crystal-field effects

Several dense Kondo compounds have a low-temperature ordered phase in which the magnetic moments are reduced with respect to the values expected for the crystal-field (CEF) ground state. In the present work the phenomenon of moment reduction is studied within a molecular-field theory combined with a variational solution of the one-impurity Anderson model with CEF effects. The calculated zero-temperature magnetization and susceptibility agree well with available exact results; the present method is easily applied to systems of any symmetry. We first study the f1 configuration in cubic symmetry, for small values of the ratio TK/Δ between Kondo temperature and CEF splitting. With a Γ∞ ground state and a field along a 〈100〉 direction, an inflection point occurs in the magnetization curve, which gives rise to a first order transition in the zero-temperature phase diagram. This feature is not found for a field along 〈110〉 or 〈111〉, for which the transition is second order. For a Γ7 ground state and small values of TK/Δ, the magnetic-nonmagnetic transition is second order for all field directions. On increasing TK/Δ an inflection point in the magnetization curve appears first for a field along 〈111〉. The theory is applied to a study of cubic CeAg, CeAl2, CePb3, CeIn3, CeTe, and hexagonal CePd2Ga3. The bare value of the moment is found to be strongly increased by exchange coupling to excited CEF states, and the amount of Kondo reduction is found to be substantial, confirming the importance of the Kondo effect in these compounds.

高濃度近藤系化合物ＹｂＣｕ５−ｘＡｇｘの磁気的，電気的性質

YbCu4Ag crystallizes in the cubic AuBe5-type structure where Yb is trivalent and shows dense Kondo behavior, while YbCu5 is known to have the hexagonal CaCu5-type structure where Yb is in a nonmagnetic divalent state. In this study, a pseudo-binary system YbCu5-xAgx was investigated. The powder Xray diffraction revealed that YbCu5-xAgx has the cubic AuBe5-type structure in the range of 0.125≤x≤1.0, while both the cubic and the hexagonal phase exist for 0≤x≤0.1, which suggests YbCu5 has also cubic AuBe5-type where Yb seems to be trivalent. Magnetic and transport properties show that YbCu5-xAgx is a dense Kondo system in which Kondo-temperature TK decreases continuously with the decrease of Ag-concentration x, causing the enhancement of the zerotemperature susceptibility x(O), the T2-coefficient A of electrical resistivity and the Sommerfeld coefficient γ of specific heat. The γ value was found to be enhanced to as large as 460mJ/mo1K2 in YbCu4.875Ag0.125. These results imply the cubic AuBe5-type YbCu5 is a dense-Kondo or a heavy-fermion system, in which γ reaches to about 500mJ/molK2.

The antiferromagnetic spin- 1/2 -XXZ model on rings with an odd number of sites

The ground-state energies of the antiferromagnetic XXZ model at a given spin are determined on chains with an odd number N of sites. Analytical and numerical solutions of the Bethe ansatz equations are compared for the N-even and N-odd case. The scaling properties of the ground-state energies enable the determination of the zero-temperature susceptibility. For the isotropic case, we analyse the logarithmic terms in the low-field limit.

Susceptibility of the one-dimensional dimerized Hubbard model.

We show that the zero-temperature susceptibility of the one-dimensional, dimerized Hubbard model at quarter-filling can be accurately determined on the basis of exact diagonalization of small clusters. The best procedure is to perform a finite-size scaling of the spin velocity ${\mathit{u}}_{\mathrm{\ensuremath{\sigma}}}$, and to calculate the susceptibility from the Luttinger-liquid relation \ensuremath{\chi}=2/\ensuremath{\pi}${\mathit{u}}_{\mathrm{\ensuremath{\sigma}}}$. We show that these results are reliable by comparing them with the analytical results that can be obtained in the weak- and strong-coupling limits. We have also used quantum Monte Carlo simulations to calculate the temperature dependence of the susceptibility for parameters that should be relevant to the Bechgaard salts. This shows that, used together, these numerical techniques are able to give precise estimates of the low-temperature susceptibility of realistic one-dimensional models of correlated electrons.

Doping dependence of the susceptibility in the two-dimensional Hubbard model close to half-filling.

We use a theory developed in a previous paper [T. Kopp and F. Mila, Phys. Rev. B 43, 12 980 (1991)] to interpret recent Monte Carlo data relative to the doping dependence of the zero-temperature susceptibility of the Hubbard model on a square lattice. According to this theory, the susceptibility does not decrease, like the density of states, but increases upon doping, the essential reason being that the hopping processes that contribute to the susceptibility are suppressed close to half-filling because the wave functions on different sublattices have a vanishing overlap in that limit. We show that, for U/t=4, this theory is in very good agreement with recent Monte Carlo data.

Mode-coupling theory for relaxation of coupled two-level systems

A Mori approach to the dynamics of coupled tunnelling units in defect crystals is presented. Transverse and longitudinal correlation functions of a two-level system are given as continued fractions; the memory kernels are evaluated in a usual decoupling approximation. Due to the random configuration of the defects on the host lattice both two-level splitting and relaxation rates show a broad distribution; the corresponding distribution function is derived for the case of a dipolar interaction of the defects. The theory covers both weak and strong coupling; the average interaction energy turns out to be the essential parameter. Dependence on frequency, temperature and concentration of the dynamical susceptibility is discussed. When passing from weak to strong coupling, the zero-temperature susceptibility shows a crossover from a constant value to a decrease with the third power of inverse defect concentration; there is quite a strong relaxational peak in the susceptibility. The theory accounts for several features observed in a recent low-frequency experiment on KCl:Li.

Alpha - gamma transition in Ce. II. A detailed analysis of the Kondo volume-collapse model.

The Kondo volume-collapse (KVC) model of the \ensuremath{\alpha}-\ensuremath{\gamma} transition in Ce metal is examined quantitatively using Anderson impurity Hamiltonian parameters obtained from electron spectroscopy. After the hybridization from spectroscopy is scaled by 1.12 to reproduce exactly the experimental zero-temperature susceptibility, the calculation, with no further adjustable parameters, predicts a phase boundary in good agreement with experiment. It is found that the cohesive energy contribution from the hybridization of unoccupied f states and conduction states is quantitatively important in Ce, with a value much larger than the Kondo energy. This contribution is equally large and important for La and Pr, for which the hybridization is often ignored. It is, however, almost spin independent, so that it does not contribute directly to the Kondo energy. Thus the 4f cohesive energy contribution is large in both the \ensuremath{\alpha} and \ensuremath{\gamma} phases, while only the Kondo spin fluctuation energy (and entropy) causes the \ensuremath{\alpha}-\ensuremath{\gamma} transition. This distinguishes the KVC model from the Mott transition model. The Anderson-Hamiltonian-based KVC model is also distinguished from the Kondo-Hamiltonian-based spin-only version of the KVC model in that the latter approach cannot make direct contact with spectroscopic data because charge degrees of freedom are ignored from the outset. This work provides a quantitative confirmation that a unified understanding of the high-energy spectroscopic and low-energy thermodynamic properties of Ce metal has been achieved at the quantitative level.

The classical susceptibility and the temperature-dependent susceptibility of a free electron gas

The origin of dimensional independence in the classical susceptibility is studied. This study has led to an integral expression for the finite-temperature susceptibility of a free electron gas, given in terms of the zero-temperature susceptibility. At finite temperatures the susceptibility is regular. The singularity, which exists at twice the Fermi wave vector when T=0, vanishes. Thus the anomalous behavior associated with 2kF is expected to disappear when T≠0.

Logarithmic singularities in the susceptibility of the antiferromagnetic SU(N) Heisenberg model.

We consider the integrable SU(N)-invariant Heisenberg model in one dimension with degrees of freedom in the symmetric rank-m tensor representation. It is shown that for antiferromagnetic coupling the zero-temperature susceptibility to an arbitrary field breaking the SU(N) invariance of the internal degrees of freedom has logarithmic singularities as the field tends to zero. The logarithms arise from the interference of the two ``Fermi points'' of the spin-wave spectrum and do not depend on the level splitting scheme. These properties hold for a variety of models, e.g., the SU(N)-invariant Heisenberg chain of spin S=(N-1)/2, the Babujian-Takhtajan model, the N-component fermion gas interacting in one dimension by a repulsive \ensuremath{\delta}-function potential, the N-component supersymmetric t-J model in one dimension, the Gross-Neveu model, and the SU(N) generalization of the Hubbard chain.